Summary: Using a topological approach, we study the dynamics of the basal membrane of mammal epidermis when basal cells detach or divide. A theoretical characterization of the steady state of the tissue, in a very good agreement with experimental data, includes for the first time the division and the disappearance of cells in a two-dimensional random cellular structure. The results obtained predict a strong correlation between the size of the attachment of basal cells to the basal membrane and their biological behaviour (division or detachment). This suggests that the main factor determining the fate of basal cells, and thus controlling the renewal of the epidermis, is the cells’ surface tension and adhesion.